Exponential Localization of Spatial Random Permutations in One Dimension
Fuente:
arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866915825924964352 |
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| author | Drogin, Reuben Hernández, Felipe |
| author_facet | Drogin, Reuben Hernández, Felipe |
| contents | We consider a class of random permutations of the interval $[-n,n]$, in which points are typically displaced a distance $O(W)$. We show the cycles are localized on the scale $W^3$, with an exponentially decaying tail bound. Analogous to eigenfunctions of one dimensional random band matrices, the cycles are conjectured to be localized to the scale $W^2.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_01242 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Exponential Localization of Spatial Random Permutations in One Dimension Drogin, Reuben Hernández, Felipe Probability We consider a class of random permutations of the interval $[-n,n]$, in which points are typically displaced a distance $O(W)$. We show the cycles are localized on the scale $W^3$, with an exponentially decaying tail bound. Analogous to eigenfunctions of one dimensional random band matrices, the cycles are conjectured to be localized to the scale $W^2.$ |
| title | Exponential Localization of Spatial Random Permutations in One Dimension |
| topic | Probability |
| url | https://arxiv.org/abs/2603.01242 |